I received my A.B and M.A. in Mathematics from the University of California, Berkeley in 1976 and 1978 respectively. In 1982 I earned my Ph.D. in Mathematics from the University of Utah under the supervision of Ronald J. Stern. After receiving my doctorate I was awarded a National Science Foundation Postdoctoral Fellowship which allowed me to visit the Courant Institute of Mathematical Sciences at New York University. Subsequently I held positions at Rutgers University, Oregon State University, and Pomona College before coming to Pitzer in 1989. I have spent time visiting the University of Melbourne, Australia, the University of Hawaii, Manoa, and the Mathematical Sciences Research Institute, Berkeley, California.
I teach a variety of lower-division courses ranging from the traditional precalculus-calculus sequence to much more unusual courses designed for the liberal arts student, such as
I also teach the following upper-division courses, usually in alternate years.
Course descriptions can be found in the Pitzer Catalog.
My research interests are primarily in knot theory and low-dimensional topology. Over the years I have collaborated on the tabulation of all prime alternating knots through 18 crossings and prime nonalternating knots through 16 crossings. (This began as a project with six high school students at Claremont High School.) Together with Morwen Thistlethwaite, we have written a program called Knotscape that allows ready access to the knot tables as well as the computation of various knot invariants such as skein polynomials, representations of the fundamental group of a knot into permutation groups, and a number of hyperbolic invariants. I have also worked on skein modules of 3-manifolds and other problems that arise from the study of the skein polynomials of knots. I am also interested in hyperbolic knots and various geometric knot invariants such as the A-polynomial of knots. Most recently I have focussed on other invariants of knots, especially ones related to representations of the knot group.
Here is a list of my publications.
During the three summers of 2005, 2006, and 2007, I was director of the Claremont Colleges Mathematics REU and directed undergraduate students in summer research projects.
I have supervised the following students' Senior Thesis in Mathematics while in Claremont.
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